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Basic study of ℜ-semigroups and their homomorphisms

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Abstract

In this paper we study ℜ-semigroups from the standpoint of their homomorphisms into the semigroup IR of positive real numbers under addition. Every ℜ+-semigroup S is isomorphic with a subdirect product of a structure group G and a semigroup of positive real numbers. It is determined by G and a positive real valued function cp on G. We also study the semigroup Hom(S,T) of homomorphisms of an ℜ-semigroup S into another ℜ-semigroup T. Each element of Hom(S,T) can be described in terms of an element of Hom(S,IR+) and an element of Hom(S,H) where H is a structure group of T.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 95616, Davis, California, USA

    Takayuki Tamura

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  1. Takayuki Tamura
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TO ALFRED H. CLIFFORD on his 65th birthday on the 11th of July, 1973

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Tamura, T. Basic study of ℜ-semigroups and their homomorphisms. Semigroup Forum 8, 21–50 (1974). https://doi.org/10.1007/BF02194744

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  • DOI: https://doi.org/10.1007/BF02194744

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